lucid.cube¶

lucid.cube(a: Tensor, /) → Tensor¶

The cube function computes the element-wise cube of each element in the input tensor.

Function Signature¶

def cube(a: Tensor) -> Tensor

Parameters¶

a (Tensor): The input tensor to be cubed element-wise.

Returns¶

Tensor:
A new tensor containing the cubed values of the elements in the input tensor. If a requires gradients, the resulting tensor will also require gradients.

Forward Calculation¶

\[\mathbf{out}_i = (\mathbf{a}_i)^3\]

Backward Gradient Calculation¶

\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = 3 (\mathbf{a}_i)^2\]

Example¶

>>> import lucid
>>> a = Tensor([1, 2, 3], requires_grad=True)
>>> out = lucid.cube(a)
>>> print(out)
Tensor([1. 8. 27.], grad=None)